Sustainable development is vital for achieving balanced progress across the economic, environmental, and health domains, and it is closely tied to the global drive for addressing climate change and environmental challenges. In this context, reaching the “Dual-Carbon” targets—carbon peaking and carbon neutrality—have become critical priorities both domestically and internationally. As a result, the cultivation of Dual-Carbon professionals is essential for driving sustainable development. This paper investigates the sustainable development capacity of Dual-Carbon professionals through an empirical study of 613 undergraduates in China utilizing Astin’s I-E-O theoretical model. This research examines the impact of course experience, self-efficacy, and learning engagement on sustainable development capacity. The results demonstrate that the course experience has a significant positive direct effect on sustainable development capacity. Moreover, self-efficacy mediates the relationship between the course experience and sustainable development capacity, while both self-efficacy and learning engagement serve as chain mediators. Based on these findings, this paper offers practical strategies to enhance the sustainable development capacity of Dual-Carbon undergraduates, providing valuable insights for the education and training of future Dual-Carbon professionals.